Q.>if x= 2/3 and x= -3 are the roots of the equation ax² +7x+b=0, find the value of a and b.

Given, and x = – 3 are the roots of the quadratic equation .

...(1)

Putting in equation (1), we get

Putting x = – 3 in equation (1), we get

⇒ 9a – 21 + b = 0

⇒ 9a + b = 21

⇒ b = 21 – 9a ...(3)

Solving (2) and (3), we get

4a + 9 ( 21 – 9a) = – 42

⇒ 4a + 189 – 81a = – 42

⇒ –77a = – 42 – 189 = – 231

⇒ a = 3

Putting the value of a in (3), we get

b = 21 – 9 × 3 = 21 – 27 = – 6

Thus, the value of a and b is 3 and – 6 respectively.